Modelling Studies on the Synthesis of Superabsorbent Hydrogels Using Population Balance Equations

Abstract

The synthesis of super-absorbent hydrogels is simulated using a kinetic model based upon population balance equations of generating functions. Dynamics in a batch reactor of properties such as the weight fraction of gel or average molecular weights of the soluble fraction can be predicted. This kinetic model neglects intramolecular cyclization reactions for simplicity (hence predictions can be valid only for very small amounts of crosslinker) but it can accommodate the operation with different kinds of crosslinking agents, namely bifunctional (e.g. N,N'-methylenebisacrylamide), trifunctional (e.g. trimethylolpropane triacrylate) and tetrafunctional (e.g. tetraallyloxyethane). The influence of the use of such different kinds of crosslinkers on the dynamics of gelation is discussed. It is also assessed the impacts of the rate propagation coefficient of the monofunctional monomer (typically acrylic acid), of the reactivity of the pendant double bonds (PDB) and of the initial composition on the dynamics of gel production. Some crucial details concerning the numerical solution of the two-point boundary value problems (TPBVP) associated with this simulation tool are also presented. Predictions of the proposed kinetic approach are compared with those obtained using the Theory of the Branching Processes which is not strictly valid with kinetically controlled polymerization systems such as those here considered. Important differences between the predictions of the two approaches are shown. Superabsorbent hydrogels were synthesized with a 2.5 L batch reactor and the experimental data are used to show that the simple kinetic model developed is able to capture the main features of this polymerization system.